هذه صورة شخصية جديدة لمقدم الطلب.

Because صورة is a feminine noun in Arabic, and the demonstrative must match it.

• هذه = this for feminine nouns
• هذا = this for masculine nouns

So:

• هذه صورة = This is a photo
• هذا كتاب = This is a book

Even though English uses this for both, Arabic distinguishes masculine and feminine.

In Arabic, the present-tense verb to be is usually omitted.

So هذه صورة شخصية جديدة لمقدم الطلب literally looks like:

• this + photo + personal + new + for the applicant

But the natural English meaning is:

• This is a new personal photo of the applicant
• or This is a new ID-style photo for the applicant, depending on context

This kind of sentence is called a nominal sentence in Arabic.

Because هذه صورة means This is a photo..., where صورة is indefinite: a photo.

Compare:

• هذه صورة = This is a photo
• هذه الصورة = This photo

So the sentence is not pointing to a specific already-known photo as a noun phrase; it is making a full statement: This is a new personal photo...

Because in Arabic, adjectives normally come after the noun they describe.

So:

• صورة شخصية جديدة literally follows the pattern
• photo personal new

In natural English, we reverse that order:

• a new personal photo

This is one of the most basic word-order differences between Arabic and English.

Because adjectives in Arabic must agree with the noun they describe.

Since صورة is feminine singular, the adjectives describing it must also be feminine singular:

• صورة = feminine singular
• شخصية = feminine singular
• جديدة = feminine singular

If the noun were masculine, the adjectives would change:

• كتاب جديد = a new book

Because the noun صورة is indefinite, so its adjectives must also be indefinite.

Arabic adjectives agree not only in gender and number, but also in definiteness.

Here:

• صورة = indefinite
• شخصية = indefinite
• جديدة = indefinite

If the noun were definite, the adjectives would also become definite:

• الصورة الشخصية الجديدة = the new personal photo

Literally, it means personal photo.

But in formal or administrative contexts, صورة شخصية often means something more specific, such as:

• an ID photo
• a passport-style photo
• a headshot used for documents

So the exact English translation depends on context. In everyday grammar terms, though, شخصية is simply an adjective meaning personal.

Literally, it means for the submitter of the application/request.

Breakdown:

• لـ = for / to / belonging to
• مقدم = submitter / one who presents
• الطلب = the request / the application

So مقدم الطلب means the applicant, and لمقدم الطلب means something like:

• for the applicant
• belonging to the applicant
• in context, often of the applicant

Yes. مقدم الطلب is an iḍāfa (possessive/genitive construction).

It literally means:

• submitter of the application

In an iḍāfa:

1. the first noun usually does not take ال
2. the second noun can be definite
3. the whole phrase becomes definite if the second noun is definite

So:

• مقدم طلب = a submitter of an application
• مقدم الطلب = the submitter of the application = the applicant

That is why you do not say المقدم الطلب here.

Because طلب can mean both request and application, depending on context.

In formal, bureaucratic, or institutional Arabic, طلب very often means:

• application
• form
• request submitted officially

So مقدم الطلب is a standard way to say applicant in formal Arabic.

A fully vowelled version would be:

هٰذِهِ صُورَةٌ شَخْصِيَّةٌ جَدِيدَةٌ لِمُقَدِّمِ الطَّلَبِ

This shows the grammar more clearly:

• هٰذِهِ = this (feminine)
• صُورَةٌ = a photo
• شَخْصِيَّةٌ = personal
• جَدِيدَةٌ = new
• لِمُقَدِّمِ الطَّلَبِ = for the applicant

The -un endings on صورة / شخصية / جديدة show that they are indefinite and in the nominative here.
The -i sound in مُقَدِّمِ and الطَّلَبِ appears because they come after the preposition لِـ, which causes the genitive.

In normal unvowelled writing, these short vowels are usually not written.